Electric force, theory and algebra.

[NihalRi]

Homework Statement

This question has two parts.
There is a quarter or radius R that is charged with a net force of Q. A point like charge of net charge q,is at a distance z from the center of the quarter.
Q1: Under what condition could we use Coulomb's law to find the magnitude the force between the quarter and the charge.
A1: My answer is when the charge on the Quarter is concentrated at its center.
Q2: In an experiment the force was found to be given by , F= Qq/A2ε°(1 -( z/(z^2+R^2)^2/2). Where A is the area of the quarter. Apply your condition from Q1 to show this equation is consistent with Coulomb/s law.
sorry it looks like a mess.

Homework Equations

none

The Attempt at a Solution

I tried to find the limit as R approaches zero. the part in the first set of brackets becomes zero, then so does the whole expression, so I was wondering if I approached this completely wrong, or if it's a matter of properly rearranging the expression. Thank you in advance.

 

[kuruman]

It's a matter of finding the limit properly. Are you familiar with Taylor series? If so, do a Taylor expansion and see what you get. If not, there is way to get around it that I can show you.

 

[NihalRi]

It's a matter of finding the limit properly. Are you familiar with Taylor series? If so, do a Taylor expansion and see what you get. If not, there is way to get around it that I can show you.

Thank you, this worked and reduced to coulomb's expression XDXDXD